Question: Divide. Write the quotient in lowest terms. $12 \div 1\dfrac15 = $
Explanation: First, let's rewrite $12$ and $1\dfrac15$ as fractions: $12 \div 1\dfrac15 =\dfrac{12}1 \div \dfrac{6}5$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{6}5$ is $\dfrac5{6}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{12}1 \div \dfrac{6}5=\dfrac{12}{1}\times\dfrac5{6}$ $=\dfrac{12\times 5}{1 \times 6}$ $=\dfrac{ \stackrel{2}{\cancel{12}} \times~ 5 }{ 1\times\underset{1}{\cancel{6}}} $ $=\dfrac{2\times 5}{1 \times 1}$ $=\dfrac{10}{1}$ We can also write this as $10$.